1 © 2014 The MathWorks, Inc.

Time Series Modeling with MATLAB

Abhishek Gupta

Application Engineer

2

Overview of Time Series Modeling

Time Series Modeling with MATLAB

Parametric Modeling - Regression

ARIMA/GARCH Modeling

Summary

Agenda

3

What is Time Series Modeling?

Use of mathematical language to make predictions

about the future

Time Series

Model

Input/

Predictors

Output/

Response

Electricity Demand

,...),,( DPtTfEL

Examples

Pairs Trading strategies

500 1000 1500 2000 2500 3000 3500 4000 450095

100

105

110

115

120

Price (

US

D)

Pairs trading results, Sharpe Ratio = 17.2

500 1000 1500 2000 2500 3000 3500 4000 4500-20

-10

0

10

20

Indic

ato

r

Pairs indicator: rebalance every 40 minutes with previous 180 minutes' prices.

500 1000 1500 2000 2500 3000 3500 4000 4500-5

0

5

10

Serial time number

Retu

rn (

US

D)

Final Return = 8.6 (7.89%)

LCO

WTI

Indicator

LCO: Over bought

LCO: Over sold

Position for LCO

Position for WTI

Cumulative Return

Q1-08 Q2-08 Q3-08 Q4-08 Q1-09 Q2-09 Q3-09 Q4-09 Q1-10 Q2-10 Q3-10 Q4-10 Q1-11 Q2-1120

40

60

80

100

120

140

160

Date

Price (

US

D)

Intraday prices for LCO and WTI

LCO

WTI

4

Overview of Time Series Modeling

Time Series Modeling with MATLAB

Parametric Modeling - Regression

ARIMA/GARCH Modeling

Summary

Agenda

5

Examples

Predicting S&P 500 (parametric)

– Multiple linear regression

– Feature selection and scenario analysis

Predicting S&P 500 (time series modeling)

– ARIMA modeling

– GARCH modeling

May-01 Feb-04 Nov-06 Aug-09 May-12

800

900

1000

1100

1200

1300

1400

1500

1600

1700

1800

S&

P 5

00

Realized vs Median Forecasted Path

Original Data

Simulated Data

-5

0

5

10

0

2

4

6

8-1.5

-1

-0.5

0

0.5

1

% Change in Crude Oil Returns

Scenario Analysis

Unemployment Rate (%)

% C

hange in S

&P

500 R

etu

rns

6

Financial Modeling Workflow

Research and Quantify

Data Analysis

& Visualization

Financial

Modeling

Application

Development

Reporting

Applications

Production

Share

Automate

Files

Databases

Datafeeds

Access

7

Example – Predicting S&P 500 Responses to

Economic Data

Goal:

– Predict changes to S&P 500

index as responses to changes

in economic data

Approach:

– Collect and “clean up” economic

and financial market data

– Model S&P 500 index returns

using multiple linear regression,

predictor selection and model

diagnostic techniques

2001 2007 2013600

800

1000

1200

1400

1600

1800

2000

S&P 500 Stock Price Index

(Index, Daily)

Response

2001 2007 20130

1000

2000

-5

0

5Equity Market-related Economic Uncertainty Index

(Index, Daily )

Leading Index f or the United States

(Percent, Monthly )

2001 2007 201302468

10

0246810

10-Year Treasury Constant Maturity Rate

(Percent, Daily )

3-Month Treasury Bill: Secondary Market Rate

(Percent, Monthly )

2001 2007 201302468

10

0246810

3-Month Eurodollar Deposit Rate (London)

(Percent, Daily )

3-Month London Interbank Of f ered Rate (LIBOR), based on U.S. Dollar

(Percent, Daily )

2001 2007 20130

1

2

50

100

150U.S. / Euro Foreign Exchange Rate

(U.S. Dollars to One Euro, Daily )

Japan / U.S. Foreign Exchange Rate

(Japanese Yen to One U.S. Dollar, Daily )

2001 2007 201302468

10

0246810x 10

5

Civ ilian Unemploy ment Rate

(Percent, Monthly )

Initial Claims

(Number, Weekly , Ending Saturday )

Predictors

-5

0

5

10

0

2

4

6

8-1.5

-1

-0.5

0

0.5

1

% Change in Crude Oil Returns

Scenario Analysis

Unemployment Rate (%)

% C

hange in S

&P

500 R

etu

rns

8

Regression Modeling Techniques

Regression

Non-linear Reg.

(GLM, Logistic)

Linear

Regression Decision Trees

Ensemble

Methods

Neural

Networks

9

Example – Predicting S&P 500 Responses to

Economic Data

Support for major data

providers

Numerous regression and

linear modeling techniques

with rich documentation

Interactive visualizations

Rapid exploration &

development

2001 2007 2013600

800

1000

1200

1400

1600

1800

2000

S&P 500 Stock Price Index

(Index, Daily)

Response

2001 2007 20130

1000

2000

-5

0

5Equity Market-related Economic Uncertainty Index

(Index, Daily )

Leading Index f or the United States

(Percent, Monthly )

2001 2007 201302468

10

0246810

10-Year Treasury Constant Maturity Rate

(Percent, Daily )

3-Month Treasury Bill: Secondary Market Rate

(Percent, Monthly )

2001 2007 201302468

10

0246810

3-Month Eurodollar Deposit Rate (London)

(Percent, Daily )

3-Month London Interbank Of f ered Rate (LIBOR), based on U.S. Dollar

(Percent, Daily )

2001 2007 20130

1

2

50

100

150U.S. / Euro Foreign Exchange Rate

(U.S. Dollars to One Euro, Daily )

Japan / U.S. Foreign Exchange Rate

(Japanese Yen to One U.S. Dollar, Daily )

2001 2007 201302468

10

0246810x 10

5

Civ ilian Unemploy ment Rate

(Percent, Monthly )

Initial Claims

(Number, Weekly , Ending Saturday )

Predictors

-5

0

5

10

0

2

4

6

8-1.5

-1

-0.5

0

0.5

1

% Change in Crude Oil Returns

Scenario Analysis

Unemployment Rate (%)

% C

hange in S

&P

500 R

etu

rns

10

Example – Time Series Modeling and

Forecasting for the S&P 500 Index

Goal:

– Model S&P 500 time series as a

combined ARIMA/GARCH

process and forecast on test data

Approach:

– Fit ARIMA model with S&P 500

returns and estimate parameters

– Fit GARCH model for S&P 500

volatility

– Perform statistical tests for time

series attributes e.g. stationarity

May-01 Feb-04 Nov-06 Aug-09 May-12

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

11000

S&

P 5

00

Realized vs All Forecasted Paths

Original Data

Simulated Data

May-01 Feb-04 Nov-06 Aug-09 May-12

800

900

1000

1100

1200

1300

1400

1500

1600

1700

1800

S&

P 5

00

Realized vs Median Forecasted Path

Original Data

Simulated Data

11

Conditional Mean

Models

Conditional Variance

Models

AR- Autoregressive

MA - Moving Average

ARIMA - Integrated

ARIMAX - eXogenous

inputs

Vector ARMA

(VARMA)

ARCH

GARCH

EGARCH

GJR

Non-Linear Models

NAR Network

NARX Network

Models for Time Series Data

12

Example – Time Series Modeling and

Forecasting for the S&P 500 Index

Numerous ARIMAX and

GARCH modeling techniques

with rich documentation

Interactive visualizations

Code parallelization to

maximize computing resources

Rapid exploration &

development

May-01 Feb-04 Nov-06 Aug-09 May-12

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

11000

S&

P 5

00

Realized vs All Forecasted Paths

Original Data

Simulated Data

May-01 Feb-04 Nov-06 Aug-09 May-12

800

900

1000

1100

1200

1300

1400

1500

1600

1700

1800

S&

P 5

00

Realized vs Median Forecasted Path

Original Data

Simulated Data

13

Overview of Time Series Modeling

Time Series Modeling with MATLAB

Parametric Modeling - Regression

ARIMA/GARCH Modeling

Summary

Agenda

14

Time Series Modeling with MATLAB

Interactive environment

– Visual tools for exploratory data analysis

– Easy to evaluate and choose best algorithm

– Simple code parallelization to maximize resources usage

– Apps available to help you get started (e.g,. import tool, database explorer, curve fitting tool)

Multiple algorithms to choose from

– Regression

– Time series analysis – ARIMAX/GARCH

– Machine learning techniques

15

Learn More: Time Series Modeling with MATLAB

To learn more, visit: http://www.mathworks.com/help/econ

/examples

Modeling the United

States Economy

16

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17

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s Im

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Questions?